Lensing properties of the einasto profile in terms of the meijer G function
Propiedades del efecto lente para el perfil de einasto en términos de la función G de meijer
Edwin Retana-Montenegro*+ Francisco Frutos-Alfaro†*
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Abstract
In N-body simulations of cold dark matter, it has been found that three-parameter models, particularly the Einasto profile, yield better fits to a wide range of dark matter haloes than two parameter models like the Navarro-Frenk-White profile. Recently, the analytical properties of the Einasto profile has been studied, allowing closed expressions for its surface mass density and lensing properties in terms of the Fox H and Meijer G functions, using a Mellin transform formalism. These expressions are valid for all values of the Einasto index in terms of the Fox H function, and valid for integer and half-integer values of Einasto index in terms of the Meijer G function. In this paper, we derive expressions for lensing properties of the Einasto profile for all rational values of the Einasto index in terms of theMeijer G function. Equivalency between these expressions and other recent results is also discussed
Keywords: cosmology; dark matter; Meijer G function.
Resumen
En simulaciones de N-cuerpos de materia oscura fría, se ha encontrado que modelos de tres parámetros, particularmente el perfil de Einasto, ofrece mejores ajustes para un amplio rango de halos de materia oscura que los modelos de dos parámetros como el perfil Navarro-Frenk-White. Recientemente, las propiedades analíticas del perfil de Einasto han sido estudiadas, lográdose expresiones cerradas para su densidad de masa superficial y propiedades de lente gravitational en términos de la función H de Fox, usando el formalismo de la transformada de Mellin. Estas expresiones son válidas para todos los valores del índice de Einasto en términos de la función H de Fox, y válidos para valores enteros y semi-enteros del índice de Einasto en términos de la función G de Meijer. En este artículo, se determinan expresiones para las propiedades de lente gravitational del perfil de Einasto para todos los valores racionales del índice de Einasto en términos de la función G de Meijer. La equivalencia entre estas expresiones y otros resultados recientes también es discutida. ]]>
Palabras clave: cosmología; materia oscura; función G de Meijer.
Mathematics Subject Classification: 33C60; 33E20.
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* Escuela de Física, Universidad de Costa Rica, San Pedro 11501, Costa Rica. E-mail: edwin@fisica.ucr.ac.cr
† Escuela de Física, Universidad de Costa Rica, San Pedro 11501, Costa Rica. E-mail: frutos@fisica.ucr.ac.cr